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%I #14 Sep 08 2022 08:46:18
%S 72,282,9000,13932,19212,22158,49920,65538,72228,78888,144408,169320,
%T 201492,201828,218460,234540,270030,296478,325080,355008,365748,
%U 411000,448872,461052,484152,504618,555522,558252,586362,622620,674058,981810,1067490,1095792
%N Numbers k such that k^7 - 1 and k^7 + 1 are semiprimes.
%C Since k^7 - 1 = (k-1)*(k^6 + k^5 + k^4 + k^3 + k^2 + k + 1) and k^7 + 1 = (k+1)*(k^6 - k^5 + k^4 - k^3 + k^2 - k + 1) (and since there is no term less than 3, so k-1 must have at least one prime factor), this sequence lists the numbers k such that k-1, k+1, k^6 + k^5 + k^4 + k^3 + k^2 + k + 1, and k^6 - k^5 + k^4 - k^3 + k^2 - k + 1 are all prime. - _Jon E. Schoenfield_, Dec 14 2016
%t Select[Range[100000], PrimeOmega[#^7 - 1] == PrimeOmega[#^7 + 1]== 2 &]
%o (Magma) IsSemiprime:=func<n | &+[d[2]: d in Factorization(n)] eq 2>; [n: n in [4..10000] | IsSemiprime(n^7-1)and IsSemiprime(n^7+1)]
%Y Cf. A105041, A108278, A261436, A268043, A276905.
%K nonn
%O 1,1
%A _Vincenzo Librandi_, Dec 09 2016
%E More terms from _Jon E. Schoenfield_, Dec 14 2016
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